3,118 research outputs found
On ℓ-adic representations for a space of noncongruence cuspforms
No full textThis paper is concerned with a compatible family of 4-dimensional ℓ-adic representations ρℓ of GQ := Gal(Q/Q) attached to the space of weight-3 cuspforms S3(Γ) on a noncongruence subgroup Γ ⊂ SL2(Z). For this representation we prove that:
1.
It is automorphic: the L-function L(s,ρℓ∨) agrees with the L-function for an automorphic form for GL4(AQ), where ρℓ∨ is the dual of ρℓ.
2.
For each prime p≥5 there is a basis hp = {hp+, hp-} of S3(Γ) whose expansion coefficients satisfy 3-term Atkin and Swinnerton-Dyer (ASD) relations, relative to the q-expansion coefficients of a newform f of level 432. The structure of this basis depends on the class of p modulo 12.
The key point is that the representation ρℓ admits a quaternion multiplication structure in the sense of Atkin, Li, Liu, and Long
Tuning the nanostructure and tribological properties of a non-ionic deep eutectic solvent with water addition
No full textHypothesis: The addition of water to a non-ionic N-oxide deep eutectic solvent (DES) composed of phenylacetic acid (PhAA) and N-dodecylmorpholine-N-oxide (MO-12) in a 1:1 M ratio (PhAA/MO-12) will promote interfacial nanostructure formation due to increased proton transfer and solvophobic interactions, leading to reduced friction. Experiments: The interfacial structure and friction of PhAA/MO-12 with water content up to 41.9 wt% were investigated at mica surfaces. Atomic force microscopy (AFM) was used to measure normal force-separation profiles, lateral images, and nanoscale friction. Findings: Conductivity increases over twentyfold with the addition of 23.6 wt% water. AFM force curves reveal that increasing water content in PhAA/MO-12 leads to a more pronounced interfacial structure with steps extending further into the bulk. High-resolution near-surface images show a well-defined sponge-like nanostructure at 23.6 wt% water, which is absent in the neat DES. The enhanced nanostructure is attributed to increased proton transfer from PhAA to MO-12 and segregation of polar and apolar domains driven by water strengthened solvophobic interactions. Friction reduces up to 72 % for >= 7.0 wt% water compared to the neat DES, due to a more robust boundary layer facilitated by water
Modular symbols over number fields
No full textLet K be a number field, R its ring of integers. For some classes of fields, spaces of cusp forms of weight 2 for GL(2;K) have been computed using methods based on modular symbols. J.E. Cremona [9] began the programme of extending the classical methods over Q to the case of imaginary quadratic fields. This work was continued by some of his Ph.D. students [35, 6, 22], and results have been obtained for some imaginary quadratic fields with small class number. More recently, P. Gunnells and D. Yasaki [18] have developed related algorithms for real quadratic fields.
The aim of this thesis is to contribute to the extension of the modular symbols method, when possible developing algorithms and implementations for effective computations. Some parts of the theory are purely algebraic and can be extended to all number fields. We generalise the theory for cusps and Manin symbols; we also describe a generalisation of Atkin-Lehner involutions and study other normaliser elements. On the other hand, all previous explicit computations for the imaginary quadratic field case were done only for specific fields. In the last part of this thesis we begin work towards a general implementation of the techniques used in this case. In particular, we are able to compute a fundamental domain of the hyperbolic 3-space for any imaginary quadratic field.
Implementations of the algorithms described in this thesis have been written by the author in the open-source mathematics software Sage [31]
Britain’s First Openly Gay Football Referee: The Story of Ryan Atkin
No full textFollowing the coming out of different sportsmen playing professional sport, this chapter focuses on the sport media’s reaction to the decision made by British football referee, Ryan Atkin, to come out as gay on 10 August 2017. Eleven sport media articles as well as the comments sections of two online media articles were analyzed to address two important research questions: (1) do traditional notions of heteromasculinity retain prominence in a culture of homophobia in British football? and (2) is the coverage of the coming out of Ryan Atkin by the sports media further evidence of a cultural shift in football that is reflective of decreasing homophobia? The findings were that the case study of Ryan Atkin is further reflective of various forms of masculinity and sexuality retaining equal cultural value among a number of key stakeholders – in this case the sports media. The chapter concludes by arguing that as an influential part of sports culture, the sports media are an important stakeholder in helping stigmatize and challenge homophobia through the articles that they publis
Global variability in leaf respiration in relation to climate and leaf traits
No full textOwen K. Atkin team : Owen K. Atkin, Keith J. Bloomfield, Peter B. Reich, Mark G. Tjoelker, Gregory P. Asner, Damien Bonal, Gerhard Bönisch, Matt Bradford, Lucas A. Cernusak, Eric G. Cosio, Danielle Creek, Kristine Y. Crous, Tomas Domingues, Jeffery S. Dukes, John J. G. Egerton, John R. Evans, Graham D. Farquhar, Nikolaos M. Fyllas, Paul P.G. Gauthier, Emanuel Gloor, Teresa E. Gimeno, Kevin L. Griffin, Rossella Guerrieri, Mary A. Heske, Chris Huntingford, Françoise Yoko Ishida, Jens Kattge, Hans Lambers, Michael J. Liddell, Christopher H. Lusk, Roberta E. Martin, Ayal P. Maksimov, Trofim C. Maximov, Yadvinder Mahl, Belinda E. Medlyn, Patrick Meir, Lina M. Mercado, Nicholas Mirotchnick, Desmond Ng, Ülo Niinemets, Odhran S. O’Sullivan, Oliver L. Philips1, Lourens Poorter, Pieter Poot, I. Colin Prentice, Norma Salinas, Lucy M. Rowland, Mike G. Ryan, Stephen Sitch, Martijn Slot, Nicholas G. Smith, Matthew H. Turnbull, Mark C. VanderWel, Fernando Valladares, Eric J. Veneklaas, Lasantha K. Weerasinghe, Christian Wirth, Ian J. Wright, Kirk Wythers, Jen Xiang, Shuang Xiang and Joana Zaragoza-Castellsabsen
Global variability in leaf respiration in relation to climate and leaf traits
No full textOwen K. Atkin team : Owen K. Atkin, Keith J. Bloomfield, Peter B. Reich, Mark G. Tjoelker, Gregory P. Asner, Damien Bonal, Gerhard Bönisch, Matt Bradford, Lucas A. Cernusak, Eric G. Cosio, Danielle Creek, Kristine Y. Crous, Tomas Domingues, Jeffery S. Dukes, John J. G. Egerton, John R. Evans, Graham D. Farquhar, Nikolaos M. Fyllas, Paul P.G. Gauthier, Emanuel Gloor, Teresa E. Gimeno, Kevin L. Griffin, Rossella Guerrieri, Mary A. Heske, Chris Huntingford, Françoise Yoko Ishida, Jens Kattge, Hans Lambers, Michael J. Liddell, Christopher H. Lusk, Roberta E. Martin, Ayal P. Maksimov, Trofim C. Maximov, Yadvinder Mahl, Belinda E. Medlyn, Patrick Meir, Lina M. Mercado, Nicholas Mirotchnick, Desmond Ng, Ülo Niinemets, Odhran S. O’Sullivan, Oliver L. Philips1, Lourens Poorter, Pieter Poot, I. Colin Prentice, Norma Salinas, Lucy M. Rowland, Mike G. Ryan, Stephen Sitch, Martijn Slot, Nicholas G. Smith, Matthew H. Turnbull, Mark C. VanderWel, Fernando Valladares, Eric J. Veneklaas, Lasantha K. Weerasinghe, Christian Wirth, Ian J. Wright, Kirk Wythers, Jen Xiang, Shuang Xiang and Joana Zaragoza-Castellsabsen
Rational points on hyperelliptic Atkin-Lehner quotients of modular curves and their coverings
No full textWe complete the computation of all Q-rational points on all the 64 maximal Atkin-Lehner quotients X0(N)∗ such that the quotient is hyperelliptic. To achieve this, we use a combination of various methods, namely the classical Chabauty–Coleman, elliptic curve Chabauty, quadratic Chabauty, and the bielliptic quadratic Chabauty method (from a forthcoming preprint of the fourth-named author) combined with the Mordell-Weil sieve. Additionally, for square- free levels N, we classify all Q-rational points as cusps, CM points (including their CM field and j-invariants) and exceptional ones. We further indicate how to use this to compute the Q-rational points on all of their modular coverings
Ask the expert: How to prevent leg ulcer recurrence when moving into compression hosiery. Leg ulceration
No full textOnce patients’ leg ulcers are healed, it
is recommended that you move them
from compression bandaging into
leg ulcer hosiery kits or maintenance
hosiery. But nurses often have
difficulty in getting patients to comply
with long-term hosiery use — which
does require a lot of commitment — and ulcers often return.
We asked Leanne Atkin, vascular nurse specialist at Mid-
Yorkshire NHS Trust, how to ensure that your patients
keep healing and remain healed when they move into
maintenance compression hosiery
Atkin, J. Myron, and Ernest R. House, The Federal Role in Curriculum Development: 1950-1980, Educational Evaluation and Policy Analysis, 3(September-October, 1981), 5-36.*
No full textTraces the history of U. S. government support for curriculum development between 1950 and 1980
Evidence that osteocyte perilacunar remodelling contributes to polyethylene wear particle induced osteolysis
No full textAbstract not availableRenee T. Ormsby, Melissa Cantley, Masakazu Kogawa, L. Bogdan Solomon, David R. Haynes, David M. Findlay, Gerald J. Atkin
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